write an explicit definition for the sequence -4,1,6,11,....

write an explicit definition for the sequence -4,1,6,11,....

$$\\\small{\text{arithmetical sequence: $d = 5$ and $a_1 = -4$ }}\\\\
\small{
\begin{array}{rclclcr}
a_1 &=& -4 \\
a_2 &=& a_1 + 1\cdot 5 &=& -4 + 5 &=& 1\\
a_3 &=& a_1 + 2\cdot 5 &=& -4 + 10 &=& 6\\
a_4 &=& a_1 + 3\cdot 5 &=& -4 + 15 &=& 11\\
\cdots \\
\mathbf{a_n }& \mathbf{=} & \mathbf{a_1 + (n-1)\cdot d \\\\
a_n &=& -4 + (n-1) \cdot 5 \\
a_n &=& -4 + 5\cdot n - 5 \\
a_n &=& -4-5 + 5\cdot n \\
\mathbf{a_n }& \mathbf{=} & \mathbf{-9 + 5\cdot n } \\
\\
\hline
\end{array}
}\\$$

$$\\\small{\text{check:}}\\
\small{\text{$
\begin{array}{rcl}
a_4 &=& -9+5\cdot 4\\
a_4 &=& -9 + 20 \\
a_4 &=& 11 \qquad \text{ okay } \\\\
\end{array}
$}}$$